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Spatiotemporal Image Correlation Spectroscopy (STICS) Theory,Verification, and Application to Protein Velocity Mapping inLiving CHO Cells

Benedict Hebert,* Santiago Costantino,* and Paul W. Wiseman*y

*Department of Physics and yDepartment of Chemistry, McGill University, Montreal, Quebec, Canada

ABSTRACT We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy(ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors(magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution ofthe full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobilecomponents, we are able tomeasure the protein transport even in the presence of a large fraction (.90%) of immobile species.Wepresent thebackground theory, computer simulations, andanalysis ofmeasurements on fluorescentmicrospheres to demonstrateproof of principle, capabilities, and limitationsof themethod.Wedemonstratemappingof flowvectors formixedsamplescontainingfluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present resultsfrom two-photon laser-scanningmicroscopy studies ofa-actinin/enhanced green fluorescent protein fusion constructs at the basalmembrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxeswith magnitudes of mm/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate themeasurement of correlated directed flows (magnitudes of mm/min) and diffusion of interacting a5 integrin/enhanced cyanfluorescent protein and a-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us togenerate complete transportmaps of proteinswithin subregions of the basalmembrane even if the protein concentration is too highto perform single particle tracking measurements.

INTRODUCTION

Fluorescence fluctuation techniques have been among the

most successful methods for quantitative measurements

inside living cells. They provide key insights into the dy-

namics and interactions of intracellular and transmembrane

proteins. The original fluorescence correlation spectroscopy

(FCS) method is based on temporal autocorrelation analysis

of fluorescence intensity fluctuations collected in time from

a tiny focal volume defined by the microscope focus of the

excitation laser beam within a sample (Elson and Magde,

1974; Magde et al., 1972). The magnitude and time decay of

the fluorescence intensity fluctuations contain information on

the concentration and dynamics of the fluorescent molecules

in the observation volume. Since the introduction of FCS,

there have been many improvements in both the technology

and computer processing power that have made possible the

analysis of increasingly complex systems. For example, the

introduction of confocal optics allowed for single molecule

detection (Rigler et al., 1993), two-photon fluorescence cross-

correlation allows measurement of the dynamics of interact-

ing molecules (Heinze et al., 2000), fluorescence correlations

between two adjacent focal volumes have been used to

determine velocity magnitude and direction in microstruc-

tured channels (Dittrich and Schwille, 2002), and scanning

FCS has been utilized to investigate protein-membrane

interactions (Ruan et al., 2004).

An imaging analog of FCS, image correlation spectros-

copy (ICS), was introduced to examine the distribution and

aggregation of cell membrane components (Petersen et al.,

1993). ICS involves spatial correlation analysis of fluores-

cence fluctuations within an image sampled using a

laser-scanning microscope (LSM). The image pixels are

effectively spatially parallel intensity measurements from

many confocal excitation volumes across the surface imaged.

The image cross-correlation spectroscopy (ICCS) technique

has also been introduced to measure transport properties

(Wiseman et al., 2004, 2000) and co-localization of two

different labeled molecules (Brown and Petersen, 1998). One

of the advantages of the image correlation techniques is that

the specific imaging timescales allow for measurements of

slow transport properties, even in quasistatic systems, as in

the case of transmembrane proteins in cells. A recent ex-

tension of the ICS family is intensity subtraction analysis,

which uses sequential uniform intensity subtraction from

confocal images to extract information about the brightest

population in a system containing a distribution of aggregate

sizes (Rocheleau et al., 2003).

One important problem in biophysics is characterizing the

motion and interactions of membrane proteins, extracellular

matrix components, and intracellular messengers involved in

the regulation of cell migration at the molecular level. As

recent studies have shown, the molecular partners involved

Submitted October 20, 2004, and accepted for publication February 7, 2005.

Address reprint requests to Paul W. Wiseman, Tel.: 514-398-5354; E-mail:

[email protected].

� 2005 by the Biophysical Society

0006-3495/05/05/3601/14 $2.00 doi: 10.1529/biophysj.104.054874

Biophysical Journal Volume 88 May 2005 3601–3614 3601

in cell migration are numerous and their interactions

complex (Lauffenburger and Horwitz, 1996). Cell migration

is a dynamic, integrated process that is coordinated both

spatially and temporally. Although numerous components

are known to interact before, during, and after the formation

of focal adhesions, less is known about the exact timing,

the number of components, and the transport mechanisms

involved in these interactions. New biophysical techniques

have begun to reveal important quantitative aspects of the

molecular mechanisms concerned. For example, fluores-

cence speckle microscopy has been used to investigate actin

polymerization at the front edge of migrating newt lung

epithelial cells (Ponti et al., 2004), and single particle

tracking (SPT) has also revealed movements of adhesion

proteins in apical cell membranes (Sheetz et al., 1989).

ICS analysis can quantify diffusion coefficients and flow

speeds of fluorescently labeled adhesion macromolecules

within the plasma membrane of living cells (Wiseman et al.,

2000). It relies on correlating the amplitude of fluorescence

intensity fluctuations arising from spontaneous variations in

molecular number within the illumination volume defined by

the focal spot of the LSM. These fluctuations arise as particle

clusters move in and out of the volume by diffusion, by flow,

or by a combination of both. However, the ICS technique is

not currently sensitive to the direction in which flowing

fluorescent entities exit the correlation volume; it only fol-

lows the temporal correlation of fluctuations irrespective of

the spatial direction of entry or exit from the focus. As a con-

sequence, ICS can measure only the magnitude of the velocity,

but not its direction.

We introduce a novel technique called space-time image

correlation spectroscopy (STICS), which is an extension of

temporal ICS. In contrast with ICS, STICS does not separate

the spatial fluctuation analysis from the temporal; instead, it

relies on a complete calculation of both the temporal and

all-spatial correlation lags for intensity fluctuations from

an LSM-sampled image series. Monitoring of the two-

dimensional average spatial correlations for every time lag

yields information on both directed flow and diffusion.

Further analysis is needed if a large immobile fraction is

present. Fourier-filtering the zero-frequency components in

time efficiently removes the immobile population contribu-

tion to the spatial correlations. Since fluorescence measure-

ments in crowded biological membranes often involve

a labeled macromolecule population undergoing diffusion

and/or directed motion in the presence of immobile fluo-

rescent species, STICS is ideal for isolating the fluctuations

due the mobile component population.

We have recently reported the first application of STICS

for cellular measurements (Wiseman et al., 2004). In this

study we present a full systematic treatment of the method to

illustrate its capabilities and limitations. We will first present

application of STICS for analyzing computer-simulated

images and fluorescent microsphere samples to demonstrate

the general approach and to determine the detection limits.

By using filtering in Fourier space to remove frequencies

associated with immobile components, we can detect

directional protein transport even in the presence of a large

fraction (.90%) of immobile species. We also present

results from two-photon laser-scanning microscopy STICS

studies of actinin/enhanced green fluorescent protein (EGFP)

fusion constructs at the basal membrane of living CHO cells.

We illustrate cases of measuring protein diffusion, protein

flow in random directions, and net flow within living cells

using STICS. We are able to quantify protein fluxes with

magnitudes of mm/s from retracting lamellar regions and

protrusions for adherent cells plated on fibronectin. We also

demonstrate the measurement of correlated directed flows

(magnitudes of mm/min) of interacting a5 integrin/enhanced

cyan fluorescent protein (ECFP) and a-actinin/enhanced

yellow fluorescent protein (EYFP) within living CHO cells

using two-color STICS.

MATERIALS AND METHODS

Computer simulations

A simulation program of laser-scanning microscopy of point emitters in

a two-dimensional system was written in IDL (RSI, Denver, CO) to test ICS

and its STICS derivative. This program allows the user to set a wide variety

of experimental system and instrumental collection parameters, including

the flow and diffusion characteristic times of several simulated fluorescent

particle populations, their densities, the laser beam characteristics, white-

noise levels, interacting fractions, image size, pixel size, time step, and

number of images. The simulations were run on standard desktop PCs.

Fluorescent microsphere preparations

Fluorescent microspheres with a radius of 0.1 mm were obtained from

Molecular Probes (Eugene, OR). The microspheres contained two different

fluorophores with the following spectral properties: 505/515 nm and

580/605 nm (absorption/emission). For sample preparation, both types of

Fluospheres were diluted by a factor of 5 in doubly distilled water, and drops

of the solution were deposited on coverslips. Particle flow was generated by

convective currents near the edge of the drop. These samples were imaged

using two-photon fluorescence microscopy (details below) to provide

images of two independent particle populations with no spectral overlap.

Using the image analysis freeware program ImageJ (National Institutes

of Health, Bethesda, MD), a separate single-channel image series of fluores-

cent spheres was then added to both channels of the image series of the

independent fluorescent particles in the mixed sample. This effectively

created an artificial interacting fraction between the two independent

fluorescent sphere populations, as the added signal from this third

superimposed image series appeared in both channels. In this way, we

were creating pixels with identical intensity in both channels, thus artificially

creating a cross-channel signal that mimicked two interacting red and green

microspheres. The fraction and the flow direction of this artificial (added)

interacting population were systematically varied before applying STICS

analysis.

Cell culture

CHO-K1 cells (a mutant cell line that is deficient in expression of the a5

integrin; Schreiner et al., 1991) along with CHO-K1 cells transfected with

visible fluorescent protein (VFP) fusions with a-actinin and/or a5 integrin

3602 Hebert et al.

Biophysical Journal 88(5) 3601–3614

were cultured in minimum essential medium supplemented with 10% fetal

bovine serum, and glutamine. For VFP-expressing cells, 0.5 mg/mL

neomycin (G418) was also added to the growth media. Cells were

maintained in a humidified, 8.5% CO2 atmosphere at 37�C. Cells were

lifted with trypsin and plated on 40-mm diameter No. 1.5 coverslips. The

coverslips were precoated with an integrin-activating extracellular matrix

protein (2, 5, or 10 mg/mL fibronectin) or with a non-integrin activating

matrix (200 mg/mL poly-d-lysine). For imaging, the samples were

maintained in CCM1 medium at 37 6 0.2�C in a Bioptechs FCS2 closed

incubation chamber (Bioptechs, Butler, PA), in combination with

a Bioptechs objective heater. Nontransfected CHO cells were used as

control samples to determine autofluorescence background levels. Cell

samples that had been fixed with 4% paraformaldehyde in PBS for 20 min

at room temperature were also prepared for each type of cell line studied.

The fixed cells were imaged in each experiment to provide a control for

any contributions from mechanical vibrations, stage translations, and laser

fluctuations.

Two-photon laser-scanning microscopy

Two-photon microscopy of the fluorescent microspheres was conducted

using an Olympus Fluoview 300CLSM/IX70 inverted microscope (Olym-

pus, Melville, NY), coupled with a Tsunami (model 3960) pulsed femto-

second Ti:sapphire laser (Spectra Physics, Mountain View, CA) pumped

by a Millennia XsJS laser. The microspheres were excited at 800 nm and

point detection was achieved with two external photomultiplier tubes

(Hamamatsu, Bridgewater, NJ). For imaging our microspheres, a 720

DCSPXR excitation dichroic mirror, a 555-dclp emission beam splitter, and

HQ525/50 HQ610/75 emission filters (all from Chroma Technology,

Brattleboro, VT) were employed for light detection. All images were

collected using a PlanApo Olympus 603 (NA 1.40) oil immersion objective

lens. Images were collected with a typical optical zoom setting of 23 cor-

responding to x and y pixel dimensions of 0.23 mm/pixel. Image time-series of

100 frames with a time delay of 0.45s between frames were collected.

Two-photon imaging of cells was conducted using a Biorad RTS2000MP

video-rate-capable two-photon/confocal microscope (Biorad, Hertfordshire,

UK), coupled with a MaiTai pulsed femtosecond Ti:sapphire laser (Spectra

Physics, Mountain View, CA) tunable over from 780 to 920 nm. The

microscope uses a resonant galvanometer mirror to scan horizontally at the

NTSC line-scan rate. Point detection is employed using one or two

photomultiplier tube(s) with fully open confocal pinholes when imaging. For

imaging EGFP in cells, the laser was tuned to a wavelength of 890 nm, and

a 560 DCLPXR dichroic mirror and an HQ528/50 emission filter were

employed for light detection. For imaging cells expressing both ECFP and

EYFP fusion proteins, the laser was tuned to 880 nm, and a D500LP dichroic

mirror and HQ485/22 and HQ560/40 emission filters were used for detection

and separation of the emitted fluorescence. All filters were from Chroma

Technology.

All image time-series were collected using a PlanApo Nikon (Nikon,

Tokyo, Japan) 603 oil immersion objective lens (NA 1.40), which was

mounted in an inverted configuration. Images having dimensions of 480

(height) 3 512 (width) pixels were collected with a typical optical zoom

setting of 23 corresponding to x and y pixel dimensions of 0.118 mm/pixel.

Image series with time delays of 1, 5, or 10 s between sequential frames and

60, 120, or 150 frames in total were collected from single cells. Individual

image frames sampled from the cells were accumulated as averages of 32

video rate scans (i.e., ;1 s per frame).

Image autocorrelation andcross-correlation analysis

Microscope image time-series volumes were viewed, and image subsections

of 162, 322, 642, 1282, or 2562 pixels in size were selected from regions of

the cell and exported for image correlation analysis using a custom

Interactive Data Language (IDL 6.0, RSI) program written for the PC.

Correlation calculations for each image time-series and nonlinear least-

squares fitting of the spatial correlation functions were performed in a

Windows environment on a 1.3-GHz processor PC using programs written

in IDL. Discrete intensity fluctuation autocorrelation functions were

calculated from the image sections as has been previously described

(Wiseman et al., 2000). The equations used for the calculation and fitting of

the normalized intensity fluctuation autocorrelation and cross-correlation

functions (both spatial and temporal) are described below.

THEORY

ICS and ICCS have been introduced in previous contribu-

tions (Petersen et al., 1993; Wiseman and Petersen, 1999).

We will provide a summary of the basic concepts behind

these techniques to introduce the theory necessary for STICS

analysis.

Generalized spatiotemporal correlation function

ICS is based on the correlation of fluorescence intensity

fluctuations measured from an observation area defined by

the diffraction-limited focal spot of the exciting laser beam in

a laser-scanning microscope. The intensity fluctuations in

fluorescence are recorded in an image series as the laser

beam is repeatedly rastered across the sample. Spatial and

temporal correlation is then applied to the image time-series.

We define a generalized spatiotemporal intensity fluctu-

ation correlation function which is a function of spatial lag

variables j and h and of a temporal lag variable t for

detection channels a and b:

rabðj;h; tÞ ¼Ædiaðx; y; tÞdibðx1 j; y1h; t1 tÞæ

ÆiaætÆibæt1t

; (1)

where dia(b)(x,y,t) is the intensity fluctuation in channel a(b)at pixel position (x,y) and time t with diaðbÞðx; y; tÞ ¼iaðbÞðx; y; tÞ � ÆiaðbÞæt, and Æ. . .æ in the denominator represent

spatial ensemble averaging over images at time t and t1t in

the time-series, and the numerator is also an ensemble aver-

age over all pixel fluctuations in pairs of images separated

by a lag-time of t. White-noise sources contribute to the nu-

merator only at zero lag (temporal and spatial), whereas they

will contribute to the average intensities in the denominator.

Correction methods dealing with white-noise and background

correlation have been reported (Wiseman and Petersen,

1999). The zero-lag amplitude value has not been weighed

for all fits in the current work.

Spatial correlation and cross-correlation

ICS has traditionally treated the cases for spatial and

temporal correlations separately. The spatial correlation

function rab(j, h, 0) is defined by evaluating Eq. 1 with zero

time-lag:

Velocity Mapping of Proteins in Cells 3603


rabðj;h; 0Þt ¼Ædiaðx; y; tÞdibðx1 j; y1h; tÞæ

ÆiaætÆibæt: (2)

These functions are typically calculated by Fourier methods

and fit to standard Gaussian functions by nonlinear least-

squares methods (Petersen et al., 1993; Wiseman and

Petersen, 1999). The Gaussian fit function for the spatial

correlation of the nth image is given as a two-dimensional

spatial correlation function,

rabðj;h; 0Þn ¼ gabð0; 0; 0Þn exp �j21h

2

v22p ab

( )1 gNabn (3)

(note that in this fitting equation and those that follow, the fit

parameters are highlighted in bold type). Fit parameters are

the zero-lag amplitude gab(0,0,0)n, the two-photon correla-

tion radius v2p ab, which is proportional to the laser-beam

horizontal radius, and the offset gNabn. For an ideal system

of non-interacting particles, the zero-lag amplitude

gab(0,0,0)n is inversely proportional to the mean number of

independent fluorescent particles in the correlation area

defined by the focus of the laser (Petersen et al., 1993). When

a ¼ b ¼ 1 or 2, Eq. 2 defines a spatial autocorrelation

function for one detection channel, and when a ¼ 1 and

b ¼ 2, Eq. 2 defines a spatial cross-correlation function be-

tween two detection channels.

Temporal correlation and cross-correlation

The temporal correlation function is given by evaluating the

generalized correlation function at zero spatial lags:

rabð0; 0; tÞ ¼Ædiaðx; y; tÞdibðx; y; t1 tÞæ

ÆiaætÆibæt1t

: (4)

Its decay will essentially depend on the temporal persistence

of the average spatial correlation of intensity fluctuations

between images in the time-series separated by a lag-time of

t as measured from an ensemble of focal spots (correlation

areas) within a sampled image area. The same equality and

inequality relationships hold for the a and b subscripts in

defining temporal auto- and cross-correlation functions as

was outlined above for the spatial case.

Decay models for correlation functions

The rate and shape of the decay of the correlation functions

will reflect any dynamic process that contributes fluctuations

on the timescale of the measurement. The actual decay

models for fluorescence correlation will depend on both the

underlying dynamics of the fluctuating process and the

geometry of the focal spot (the point-spread function;

Thompson, 1991). We consider four separate functional

forms that are analytical solutions for the generalized

intensity fluctuation correlation function appropriate for

specific cases of two-dimensional transport phenomena as

measured within a membrane system illuminated by a TEM00

laser beam with Gaussian transverse intensity profile. See

below.

Two-dimensional diffusion

rabð0; 0; tÞ ¼ gabð0; 0; 0Þ 11t

td

� ��1

1 gN ab: (5)

Two-dimensional flow

rabð0; 0; tÞ ¼ gabð0; 0; 0Þexp � jvf jtÆv2p abæ

� �2( )

1 gNab: (6)

Two-dimensional diffusion and flow for a single population

rabð0; 0; tÞ ¼ gabð0; 0; 0Þ 11t

td

� ��1

3exp � jvf jtÆv2p abæ

� �2

11t

td

� ��1( )

1 gN ab: (7)

Two-dimensional diffusion and flow for twopopulations (i 5 1, 2)

rabð0; 0; tÞ ¼ gabð0; 0; 0Þ1 11t

td1

� ��1

1 gabð0; 0; 0Þ2 exp � jvf2jtÆv2p abæ

� �2( )

1 gN ab:(8)

The highlighted fit-parameters are the zero-lag amplitude

gab(0,0,0), the offset gNab, the characteristic diffusion decay

time td, and the mean speed of the particles jvfj,

jvf j ¼v2p ab

tf; (9)

where tf is the characteristic flow time. The effective e�2

correlation radius Æv2p abæ is calculated by averaging the

individual v2p ab obtained from fitting Eq. 3 for every image

in the time-series. The best fit characteristic diffusion time

combined with the average correlation radius allows calcu-

lation of the diffusion coefficient:

Dexp ¼Æv2p abæ

2

4td: (10)

It is important to distinguish v2p, the effective two-photon

e�2 correlation radius, and v0, the e�2 beam radius, because

v2p is equal to v0 divided by the square-root of 2. Note that

in Eq. 9, the mean speed jvfj is directionally blind (a velocitymagnitude). ICS is not sensitive to the direction in which

the particles escape the correlation area, because the basic

3604 Hebert et al.


analysis does not include non-zero spatial lags with the

temporal lags (see Eq. 4).

Space-time image correlation andcross-correlation spectroscopy (STICS)

The object of the current work is to extend ICS and ICCS to

obtain flow vectors, or essentially to determine the direction

in which the particles are exiting the correlation areas if

directed flux is present. To achieve this, one must combine

the spatial information imbedded in the two-dimensional

spatial correlations with the time-dependent transport

measured by the temporal correlation. For this we define

a discrete approximation to the full space-time correlation

function as

r0abðj;h;DtÞ ¼

1

N�Dt+

N�Dt

t¼1

Ædiaðx;y; tÞdibðx1j;y1h; t1DtÞæÆiaætÆibæt1Dt

;

(11)

where N is the total number of images in the time-series. The

value r9ab represents the average cross-correlation function

for channels a and b, for all pairs of images separated by

a lag-time of Dt. This generalized space-time correlation

function can be considered as a time-series, where the images

are averaged two-dimensional spatial (cross-)correlation

functions, and the time variable is actually the lag-time

(Dt) between all images pairs for which the correlation was

computed.

For an image time-series collected using an LSM, r9aa(j, h,0) is the average spatial autocorrelation function from each

image (Eq. 1 averaged for each image n in the series; see Fig.

1). It will appear as a two-dimensional Gaussian with peak

value at (j¼ 0,h¼ 0). Assuming that the temporal resolution

is sufficiently high for intensity fluctuations to be correlated

between successive images, r9aa(j, h, 1), r9aa(j, h, 2), . . . arealso going to appear as Gaussian spatially distributed

correlations. However, if some particles havemoved between

frames, the correlation function is going to change depending

on the kind ofmicroscopicmotion undergone by the particles.

The simplest case is to imagine the particles as stationary, then

the correlation stays unchanged forDt¼ 0 toN and centered at

(j ¼ 0, h ¼ 0). If we now consider the particles as diffusing,

they will tend to exit the correlation area in a symmetric

fashion, thus broadening the correlation Gaussian in every

direction, analogous to a tracer diffusion experiment. The

peak will stay centered at (j ¼ 0, h ¼ 0) but its value will

decrease hyperbolically (see Eq. 5). Finally if the particles

are flowing uniformly, the spatial correlation Gaussian peak

is going to maintain its original shape as a function of time,

but its peak valuewill be shifted to lag positions (j¼�v3Dt,h ¼ �vy 3 Dt) where vx and vy are the x and y velocities ofthe particles. This is consistent with the observation that for

a flowing population, the temporal autocorrelation function

raa(0, 0, t) decays as a Gaussian. The negative signs in the

expression for j and h arise from the fact that the Gaussian

correlation peak moves in a direction opposite to the flow.

FIGURE 1 Schematic illustration of the

algorithm used to compute the discrete approx-

imation to a generalized spatiotemporal corre-

lation function for a simulated system with flow

and diffusion. The Gaussian autocorrelation

peaks for each image are shown in the left

column (Dt ¼ 0), the cross-correlation for a

lag-time of 1 time-unit in the middle column

(Dt¼ 1), and for the second longest lag-time of

N–1 time-units in the right column (Dt ¼ N–1,

where N is the number of frames in the image

series). The open arrows on the simulation

images represent the direction of the flow. The

averaged Gaussian correlation functions r9aa(j,

h, Dt) are shown at the bottom for Dt¼ 0,1 and

N–1. The separation of the Gaussian correlation

peak due to flow (FG) from the Gaussian

correlation peak arising from the diffusing

population (DG) is clearly seen.



This analysis is only valid as long as the particles undergoing

concerted motion stay within the bounds of the analyzed

region. The two-population combined case of a flowing and

diffusing population is illustrated in Fig. 1, where the

diffusion spatial Gaussian correlation peak (DG) broadensand stays centered at (j¼ 0, h¼ 0) and the flowing Gaussian

correlation peak (FG) shifts in a direction opposite to the flowof the particles (as indicated by the open arrows on the

simulated images). In this case the flowing and diffusing

populations were equally represented (in terms of density and

intensity); however, in the cell system in this study the

actively transported subpopulation is usually a small fraction

of the total dynamic species population. This effectively

makes tracking the flowing Gaussian difficult, as it is hard to

resolve near the zero-lags origin due to the diffusing and

immobile populations. A solution to this problem is presented

in the next section.

Immobile population removal

The most general case is a combination of diffusion, flow,

and immobile populations. The challenge is to extract the

velocity direction by following the flow Gaussian correlation

peak, without influence from the correlations of the im-

mobile or slowly diffusing populations (which effectively

remain centered at (0, 0) spatial lags). The immobile

population contribution to r9aa(j, h, Dt) can be removed by

Fourier-filtering in frequency space the DC component for

every pixel trace in time before running the space-time

correlation analysis. The intensity values in channel a for

a given pixel value, say ia(0, 0, t), contains contributions tothe signal of interest from dynamic and immobile component

signals and spurious white-noise sources. The signal from

dynamic components (flow and diffusion) contribute in-

tensity fluctuations that change as a function of time for

a given pixel trace. However, an immobile component only

adds a constant intensity offset to the single pixel intensity

trace through time, so removing the DC frequency

component eliminates this contribution from the correlation

analysis. For a given pixel location (x,y), the corrected

intensities are given by

i0aðx;y; tÞ ¼F

�1

f fFtfiaðx;y; tÞg3H1=Tðf Þg; (12)

where T is the total acquisition time of the image series,

H1/T(f) is the Heavyside function which is 0 for f, 1/T and 1

for f . 1/T, Fð�1Þi denotes the (inverse) Fourier-transform

with respect to variable i, and f is the pixel temporal-

frequency variable.

RESULTS AND DISCUSSION

Simulations

Using our laser-scanning microscopy simulation program

(see Materials and Methods) we ran three different sets of

simulations for point particles, exhibiting i), pure flow with

vx¼�0.12 mm/s and vy¼ 0.08 mm/s; ii), pure diffusion withD¼ 0.01 mm2/s; and iii), a two-population (one flowing, onediffusing) combination with vx ¼ �0.12 mm/s, vy ¼ 0.08

mm/s, and D ¼ 0.01 mm2/s. Fig. 2 A shows the results of

STICS analyses (without any Fourier-filtering) performed on

these simulations. All the populations are set to have the

same total number of particles (density of 50 particles/mm2),

with equal quantum yields. All simulations are 128 3 128

pixels at a resolution of 0.06 mm/pixels, and 500-frames-

long, with a time step of 0.02 s/frame. The beam radius is set

at 0.4 mm. The consequences of flow or diffusion on the

evolution of the two-dimensional contour plot of the cor-

relation function are evident. As expected in simulation i, theGaussian flow correlation peak shifts with a direction oppo-

site to the flow, and in simulation ii, the central Gaussian

correlation peak broadens due to diffusion. In the combined

case of simulation iii, the flow and diffusion the Gaussian

peaks are initially superimposed and they separate after the

flowing population has moved by more than a correlation

radius.

The temporal-decay of the zero spatial lags center of these

contours is r9aa(0, 0, t) (where channel a denotes a single

collection channel for these simulations); i.e., the temporal

autocorrelation function (Eq. 4) This is shown for simu-

lations i–iii (Fig. 2 B). Once again, we can clearly distinguishbetween the various types of transport. The Gaussian profile

of Eq. 6 (squares) is fitted to give a velocity magnitude of

0.152 6 0.004 mm/s and the fit to the hyperbolic profile of

Eq. 5 (triangles) yields a diffusion coefficient of 0.008 6

0.002 mm2/s via Eq. 10. Notice that the velocity magnitude is

close to the input value, but there is no directional infor-

mation to be gathered from the ICS analysis. The analysis

of the combined case (open circles) provides information

on the motion of both populations, with a fit (Eq. 9) velo-

city of 0.144 6 0.004 mm/s, and a diffusion coefficient of

0.009 6 0.002 mm2/s.

Performing STICS on simulation i yields peak positions

for the two-dimensional correlation Gaussian (Fig. 2 C,squares). Fitting for the x- and y-peak displacements

provides an estimate of vx ¼ �0.119 6 0.002 mm/s and

vy ¼ 0.0792 6 0.0005 mm/s. The analysis of the central

diffusion peak in simulation ii provides an estimate of the

accuracy of our results for these simulations. The x and yvelocities should be zero and they are found to be vx ¼0.006 6 0.01 mm/s and vy ¼ �0.007 6 0.006 mm/s (Fig. 2

C, triangles). Moreover, the STICS analysis applied to

simulation iii without modification is not accurate, because

of the perturbation to the velocity analysis due to the presence

of the second Gaussian correlation peak for the diffusing

population, which is centered at (j ¼ 0, h ¼ 0). In the

situation where both flowing and diffusing populations are

present, there are two cases where STICS analysis can still be

performed accurately (see Fig. 3). First, if the diffusing

population is fast compared to the directional flow, then its

3606 Hebert et al.


effects on the flow correlation peaks will be short-lived as the

central Gaussian will decay quickly. Second, if the diffusing

population is slow, it can be considered as quasi-immobile

and its intensity contribution is also going to be mostly

eliminated by the Fourier-filtering described previously. To

determine the timescales where these problems would arise,

we performed simulations where we systematically varied

the diffusion coefficient while keeping the velocity of the

particles fixed. These simulations showed that the STICS

analysis is still valid when the characteristic diffusion time is

approximately five times faster or slower than the flow

characteristic time (see Fig. 3). In simulation iii (Fig. 2 A),the diffusion is neither fast nor slow compared to the flow,

and the time-evolving Gaussian correlation peak can be fit to

FIGURE 2 STICS and ICS analysis results for computer-generated

simulations. (A) A contour plot of the STICS correlation functions for

the case of i), flow (vx ¼ �0.12 mm/s and vy ¼ 0.08 mm/s); ii), diffusion(D¼ 0.01 mm2/s); and iii), two-populations’ flow and diffusion (vx ¼�0.12

mm/s, vy ¼ 0.08 mm/s, and D ¼ 0.01 mm2/s). (B) The ICS temporal

autocorrelation functions (Eq. 4) and best fits for the same simulations. (C)

Plots of the peak position of the STICS Gaussian correlation peaks from A as

a function of time. The peak position versus time gives an estimate of the

concerted velocity of the particles in case i, of vx ¼ �0.119 6 0.002 mm/s

and vy ¼ 0.0792 6 0.0005 mm/s and in case iii, of vx ¼ �0.096 6 0.007

mm/s and vy ¼ 0.068 6 0.006 mm/s, respectively. All simulations were

128 3 128 pixels with 500 frames at a density of 50 particles/mm2, using

0.02 s/frame, 0.06 mm/pixel, and an e�2 radius of 0.4 mm.

FIGURE 3 STICS analysis results for computer simulations of two

populations, one flowing (vx ¼ �0.12 mm/s and vy ¼ 0.08 mm/s) and one

diffusing (varying diffusion coefficients). (A) The x velocity as resolved by

STICSwith and without the immobile population filtering. (B) The y velocity

as resolved by STICS with and without the immobile population filtering. On

both graphs, each point and error bar represents the average result of 100

simulations with standard deviation. The shaded regions show the set

velocities in the simulation with an acceptable error of610%. The computer

simulations were 128 3 128 pixels with 100 frames at a density of

100 particles/mm2, using 0.1 s/frame, 0.06 mm/pixel, and an e�2 radius of

0.4 mm.



give vx ¼ �0.096 6 0.007 mm/s and vy ¼ 0.068 6 0.006

mm/s (Fig. 2 C, circles) after Fourier-filtering. Notice that thex and y velocities are slightly smaller in this combined case

than for the flow-only case. This is because the remnants of

the diffusing population contribution effectively weight the

flowing Gaussian back toward the zero-lags center when we

try to fit the position of the Gaussian peak. In such a scenario,

if one can assume that the total flow is dominated by the

directional flux (as opposed to separate flows in random

directions), then one can scale the x and y velocities from

STICS analysis according to the total velocity obtained by

ICS analysis to get vx ¼ �0.118 6 0.008 mm/s and vy ¼0.083 6 0.007 mm/s. Note that the temporal ICS analysis

will be sensitive to all flow processes present, which will all

contribute to the decay of the correlation function. For the

case of the adhesion protein transport at the membrane in

cells that we report in this study, the second scenario of faster

diffusion (tD , tf) was usually observed.

If the flowcharacteristic time is slow compared to the image

acquisition rate, then some analysis artifacts are introduced by

the Fourier-filtering, which complicates the case of a slowly

flowing population. If the particles do not move more than

a correlation radius over the time of acquisition of the entire

image-series, then removing the DC offset will spatially

anticorrelate the intensities over a short distance in the

direction of the flow. In otherwords, the centralGaussian peak

is reduced in width, and accompanied by two diametrically

opposed depressions aligned with the flow direction. Never-

theless, these artifacts are of no real consequence in the

determination of the flow direction because a Gaussian can

still effectively be fit to the correlation functions. Moreover,

we can neglect signal fluctuations due to bleaching in flow/

diffusion measurements as long as the characteristic times

associated with these processes are shorter than the bleaching

time (simulation results not shown). This was the case for the

cell measurements reported below.

Fluorescent microspheres

Fluorescent microsphere samples containing a mixture of

flowing spheres emitting at two different wavelengths

(referred to as red and green) were prepared and imaged

by two-photon laser-scanning microscopy (see Materials and

Methods) to generate an image series of two independent

particle populations (referred to as non-interacting). By

adding another image series of flowing microspheres to both

independent channels in the collected time-series, we could

effectively introduce an artificial interacting population. The

direction of flow of the interacting population added by

image processing was chosen by the user and is thus

independent of the direction of flow of the original non-

interacting particle populations. A typical image from this

image-processed time-series is shown in Fig. 4 A. It has anequal density of red and green microspheres, with ;40% of

each population interacting. Such an image time-series was

then analyzed with two-color STICS, yielding directional

flow information for the red and green populations, as well as

for the interacting fraction. We can recover the flow

directions of the non-interacting red and green microsphere

populations to within 8� in the presence of the interacting

population, as compared with the recovered flow directions

of the original image time-series (i.e., analysis performed

without the addition of the interacting population). More-

over, we can find the direction of flow of the interacting

population to within 5�. Fig. 4 B shows the one-to-one

FIGURE 4 (A) A composite image of fluorescent microspheres consisting

of two different fluorescent particle populations (red and green) and an

added interacting particle population (yellow overlap). The composite image

was made by adding an independent image of fluorescent spheres (our

artificial interacting population) to both detection channel images. For each

image time-series constructed, the velocities of the non-interacting popula-

tions remained constant whereas the interacting fraction’s direction of flow

was systematically changed. (B) A plot of the interacting population velocity

magnitudes in x and y measured by STICS in the composite image series

(i.e., with the added population and the red and green microspheres present)

versus the velocity magnitude of the introduced interacting population

measured by STICS in its original image series (i.e., without the red and

green particles present).

3608 Hebert et al.


relationship between the recovered velocity magnitudes (in xand y) for the added population as measured by STICS from

the image time-series before the addition and the velocity

magnitude of the added (interacting) population as measured

by STICS in the dual-channel constructed image time-series

in the presence of the non-interacting microsphere popula-

tions. The data are plotted for several experiments in which

the direction of flow of the added interacting population was

different in each case. The magnitudes of the velocities

measured by STICS analysis on the dual-channel image

time-series differ by ,10% from the original values (as

measured separately before the addition of the artificial

interacting population; see Table 1). Note that the density of

the added interacting particle population was five times lower

than the density of each independent fluorescent particle

population.

The STICS analysis for the single non-interacting

populations is influenced by both the fraction that is flowing

independently and the movements of the interacting fraction.

As long as the overall contribution to the image intensity

from the interacting population does not exceed that of the

non-interacting population, STICS can detect the differences

in flow direction between the populations. In the case where

this effect becomes dominant (i.e., equal contribution from

interacting and non-interacting species), one can fit two

Gaussians in r9aa(j, h, t) (a ¼ 1 or a ¼ 2) to extract the two

flow directions. Conversely, the STICS analysis of the

interacting population can also be influenced by the single

non-interacting populations if these flow in the same

direction and random spatial cross-correlations occur. These

effects account for the errors in magnitude and direction of

the measured velocities in the constructed image series as

compared with the velocities measured from the original

image series of the independent microspheres.

Velocity mapping of protein transport inliving cells

We measured the phenomena of directed and nondirected

transport in living cells expressing adhesion protein EGFP

fusion constructs using STICS. We first measured a-actinin/

EGFP constructs expressed in CHO-K1 cells plated on

fibronectin. The protein a-actinin is a cytoplasmic molecule

that binds to the integrins at the membrane and also links the

actin cytoskeleton (Lauffenburger and Horwitz, 1996). We

have previously determined that a-actinin is more mobile in

the peripheral regions of the CHO cells where there is active

lamellar extension, retraction, and membrane ruffling when

the cells are activated on fibronectin (Wiseman et al., 2004).

We focused our measurements on such active peripheral

areas (see Fig. 5).

Fig. 6 shows the ICS and STICS analysis results for

a typical 643 64 pixel region from the cell periphery (Fig. 5

A). As is evident from Fig. 6 B, the temporal autocorrelation

function can be fit very well by Eq. 5, which yields a

diffusion coefficient of (9 6 1) 3 10�4 mm2/s. We show

contour plots of the Gaussian correlation peaks for different

time lags in Fig. 6 A for i), the unmodified image time-series

(without the immobile population removed); and ii), the

filtered image time-series (with the immobile population

removed). As expected, in both cases the correlation peaks

stay centered at zero spatial lags (indicated by the whitecrosshairs). Fitting for the displacement of the Gaussian

yields a very small velocity vSTICS ¼ (1.2 6 0.8) 3 10�3

mm/s (from vx ¼ (�0.9 6 0.8) 3 10�3 and vy ¼ (�0.8 6

0.7) 3 10�3 mm/s, see Fig. 6 C), which can be attributed to

either a real but very slow concerted flux of the proteins, or to

an experimental artifact such as a slow stage drift. These

values are on the order of the precision of our measurements,

which was assessed by applying the STICS analysis to cells

fixed in 4% paraformaldehyde. The corresponding values

vx ¼ (0.4 6 0.3) 3 10�3 and vy ¼ (0.2 6 0.3) 3 10�3 mm/s

establish our detection limits. These results illustrate a mem-

brane region consisting mainly of protein-diffusing and im-

mobile proteins, and show how the random walk is manifest

in both the ICS and STICS analyses.

The same analyses were applied to a different region from

the periphery of another cell (Fig. 5 B) and reveal different

protein transport. Fig. 7 shows our results for a 128 3 128

pixel region in which clusters of a-actinin are clearly

TABLE 1 STICS-measured parameters for a microsphere-image time-series (see Fig. 3)

First population

velocity (mm/min)

Second population

velocity (mm/min)

Added population

velocity (mm/min)

Interacting population

velocity (mm/min)

Set # vx vy vx vy vx vy vx vy

1 0.11 6 0.04 �1.53 6 0.05 0.14 6 0.05 �1.48 6 0.05 �0.01 6 0.05 �3.9 6 0.1 �0.01 6 0.09 �4.2 6 0.2

2 0.27 6 0.05 �1.24 6 0.04 0.30 6 0.03 �1.22 6 0.05 1.39 6 0.04 0.09 6 0.04 1.21 6 0.07 �0.25 6 0.08

3 0.03 6 0.01 �1.0 6 0.1 0.16 6 0.03 �1.23 6 0.05 �1.26 6 0.03 2.27 6 0.03 �1.08 6 0.04 2.13 6 0.04

4 0.03 6 0.06 �1.08 6 0.06 0.11 6 0.09 �0.98 6 0.04 �1.44 6 0.03 0.60 6 0.01 �1.33 6 0.03 0.52 6 0.03

5 0.02 6 0.05 �1.27 6 0.03 0.03 6 0.05 �1.20 6 0.05 �0.31 6 0.03 �1.05 6 0.02 �0.22 6 0.05 �1.02 6 0.04

6 0.12 6 0.02 �0.51 6 0.05 0.17 6 0.03 �0.63 6 0.05 0.21 6 0.02 0.98 6 0.02 0.19 6 0.02 1.00 6 0.02

The column Added population velocity refers to the STICS analysis results before image addition when applied to the single-channel image time-series that is

subsequently added to the dual-channel image time-series to create an interacting population. The column Interacting population velocity refers to the two-

color STICS analysis results after image addition for the co-localized (interacting) population in the composite image. These values should, in theory, be

equal to the values in the column Added population velocity.



resolved, and these clusters can be observed to flow in

a directed fashion on what appear to be defined linear tracks.

However, the ICS (Fig. 7 B) and STICS (Fig. 7, A and C)analyses yield very different values for flow: vICS ¼ (136 1)

3 10�3 mm/s and vSTICS ¼ (1.1 6 0.7) 3 10�3 mm/s (from

vx ¼ (�0.676 0.02)3 10�3 and vy ¼ (�0.96 0.8)3 10�3

mm/s). The total velocity value for ICS is approximately 10

times higher than the velocity value measured by STICS.

This is due to the fact that STICS only measures the net

resultant directed component (here the majority, but not all of

the clusters, were observed to be traveling to the left and

down in the image series), whereas ICS measures an average

total flow speed (and a small diffusion coefficient in this

case). Hence the combination of ICS and STICS allows us to

distinguish between directional flow in one direction (see

also Fig. 8), or directional flow in many random directions as

was the case here. Visual tracking of the resolved clusters

shows that the directions are random, with more moving

toward the lower left of the image. In this case, single particle

tracking (SPT) analysis will, in principle, provide more in-

formation about the range of transport (Saxton and Jacobson,

1997). However, it proved difficult to track the clusters with

the fluorescence signal/noise and for the density of expres-

sion of EGFP proteins typical for these transfected cells (SPT

data not shown).

The true advantage of STICS emerges in situations where

no bright clusters are clearly resolved (hence SPT would be

impossible), but concerted flux of protein can be detected

by correlation analysis. Fig. 8 shows analyses results for a

128 3 128 pixel region of a basal membrane of a CHO cell

FIGURE 5 Two-photon LSM images

of the basal membrane of CHO cells

expressing EGFP-labeled a-actinin. The

regions analyzed with ICS and STICS are

shown as open squares and the STICS

analysis results are shown in Figs. 5–7.

(A) A 642 pixel region where the temporal

autocorrelation function is best fit to a

single-population diffusion model (Eq.

5). (B) A 1282 pixel region where the

temporal autocorrelation function is best

fit to a two-population flow/diffusion

model (Eq. 8). (C) A 1282 pixel region where the temporal autocorrelation function is best fit to a two-population flow/diffusion model (Eq. 8). All

images are 512 3 480 pixels at a resolution of 0.118 mm/pixel, and a total of 180, 360, and 120 frames at a resolution of 5, 5, and 15 s/frame for A–C,

respectively.

FIGURE 6 In vivo ICS and STICS

analysis of protein diffusion in a peripheral

basal membrane region of a CHO cell (Fig.

5 A) expressing EGFP-labeled a-actinin.

(A) Contour plots of space-time correlation

functions from STICS analysis (Eq. 11) as

a function of lag-time for i) with and ii)

without the immobile population contribu-

tion present. (B) A plot of the ICS temporal

autocorrelation function and best fit to a

single-population diffusion model (Eq. 5).

The recovered diffusion coefficient was

D¼ (96 1)3 10�4mm2/s. (C) Peak trackingplot of the STICS correlation peaks reveals

that they stay centered at zero spatial lags,

within the precision of our measurement.

3610 Hebert et al.


expressing EGFP-labeled a-actinin (Fig. 5 C). Here the ICSanalysis again detects flow and diffusion of two separate

populations (Fig. 8 B) with vICS ¼ (7.7 6 0.8) 3 10�3 mm/s

and a small diffusion coefficient D ¼ (66 1)3 10�5 mm2/s.

The STICS analysis also detects a directional flow (Fig. 8, Aand C) with vx ¼ (1.86 0.3)3 10�3 and vy ¼ (5.56 0.2)3

10�3 mm/s. This example illustrates the importance of remov-

ing the immobile population, since the Gaussian correlation


analysis of protein flux in random

directions in a peripheral basal mem-

brane region of a CHO cell (Fig. 5 B)

expressing EGFP-labeled a-actinin. (A)

Contour plots of space-time correlation

functions from STICS analysis as

a function of time for i) with and ii)

without the immobile population con-

tribution present. (B) A plot of the ICS

temporal autocorrelation function and

best fit to a two-population flow/dif-

fusion model (Eq. 8). The recovered

ICS velocity and diffusion were vICS ¼(136 1)3 10�3 mm/s andD¼ (86 1)

3 10�4 mm2/s. (C) Peak tracking plot

of the STICS correlation peaks reveals

that they stay centered at zero spatial

lags, within the precision of our mea-

surement, yielding a very small velocity

of vSTICS ¼ (1.1 6 0.7) 3 10�3 mm/s.


analysis of directed protein flow in

a peripheral basal membrane region of

a CHO cell (Fig. 5 C) expressing

EGFP-labeled a-actinin. (A) Contour

plots of space-time correlation func-

tions from STICS analysis as a function

of time for i) with and ii) without theimmobile population contribution pres-

ent. (B) A plot of the ICS temporal

autocorrelation function and best fit to

a two-population flow/diffusion model

(Eq. 8). The recovered velocity was

vICS ¼ (7.7 6 0.8) 3 10�3 mm/s and

a small diffusion coefficient was mea-

sured: D ¼ (6 6 1) 3 10�5 mm2/s. (C)Peak tracking plot of the STICS

correlation peaks (after the immobile

population removal) shows a net dis-

placement of the Gaussian center,

yielding velocities of vx ¼ (1.8 6 0.3)

3 10�3 and vy ¼ (5.5 6 0.2) 3 10�3

mm/s.



peak in Fig. 8 A i) is dominated by immobile protein

population spatial correlations and thus stays centered at

zero spatial lags. However, after the immobile population

removal, one can see the Gaussian peak clearly moving away

from the zero lags center toward the bottom left corner in

a directed fashion and the residual central peak from the

diffusion population (Fig. 8 A ii).The formation and disassembly of adhesions as lamellar

protrusions are extended or retracted must result in some

form of transport of adhesion macromolecules into or out of

the transient lamellar extension. Fig. 9 shows the heteroge-

neous spatial distribution of a-actinin in another CHO cell,

close to the edge where lamellar protrusions are clearly

visible in the lower part of the image. During the course of

this 60-frame (300 s) image series, the protrusions retract and

adhesion structures disassemble. STICS analysis shows that

there is a net flux of proteins directed toward the interior of

the cell (Fig. 9, arrows), with the average flow rate of 0.226

0.04 mm/min (see Table 2), in agreement with rates of

filamentous actin retrograde flow (Vallotton et al., 2003).

ICS analyses on the same regions show greater variations in

the total velocity measured (50% spread versus 17% for

STICS). However, given the relatively small size of these

regions (162 or 322 pixels) it was hard to determine fit

parameters to the temporal autocorrelation function with

high precision as the signal/noise ratio depends on the

number of independent fluctuations sampled (Meyer and

Schindler, 1988). STICS is not as sensitive to spatial

sampling as ICS because we are simply tracking a Gaussian

peak, which is far easier than fitting a noisy temporal

autocorrelation curve with a three-parameter hyperbola or

Gaussian. Hence the discrepancy between the two analyses

is due to the better performance of STICS in this small spatial

sampling regime. In the case of ruffling membranes,

however, surface height variations are going to lead to

intensity variations due to the intensity distribution of the

point-spread function and we exclude such regions from

analysis. Such variations are detected as changes in the fit

radius of the spatial correlation functions (Wiseman et al.,

2004). Fluorescent speckle microscopy (FSM) has also been

used to investigate filamentous actin flow at the leading edge

of migrating cells (Vallotton et al., 2003). Tracking very

small amounts of a fluorescent derivative of the monomer

that forms the actin filaments allowed the authors to generate

retrograde actin flow maps with excellent spatial resolution

(1 mm2 regions, or;82 pixels in our case). The advantage of

FSM is that it does not average flow directions because it

follows the trajectories of single speckles, hence it can have

greater precision in regions where there is flow in several

directions. However, FSM requires specialized fluorescent

labeling techniques, whereas STICS can be used without

special labeling (i.e., standard VFP transfected cells) using

standard LSM imaging approaches with approximately the

same spatial resolution.

Another advantage of the STICS method is that it can be

carried out in a cross-correlation scheme, with dual color

labeling of different macromolecular species. If the zero

time-lag cross-correlation function is non-zero, it means that

the proteins are interacting in a common complex (Wiseman

et al., 2004). Furthermore, if we monitor the spatial cross-

correlation peaks in subsequent time lags, then we can

determine if the proteins are flowing or diffusing together.

We imaged CHO cells expressing a5 integrin/EYFP and

a-actinin/ECFP using two-photon microscopy and dual

channel detection, and analyzed the spatiotemporal inten-

sity fluctuations from both channels via two-color spatio-

temporal image cross-correlation spectroscopy (STICCS).

FIGURE 9 Two-photon STICS velocity map image of EGFP/a-actinin

flux in the vicinity of a retracting lamellar extension in a CHO cell plated on

fibronectin. The original image-series reveals that the extended lamellar

protrusions are retracting. Selecting regions of 16 3 16 or 32 3 32 pixels

and performing the STICS analysis reveals a net flow of the a-actinin toward

the cell interior (arrows). The spatial scale is shown as a bar and the velocity

scale is shown as an arrow. The original image-dimensions are 512 3 480

pixels at 0.118 mm/pixel and a total of 120 images at 5 s/frame.

TABLE 2 STICS-measured parameters for image regions of a CHO cell (see Fig. 7)

Region 1 2 3 4 5 6 7 8

vx (mm/min) �0.07 6 0.04 �0.06 6 0.01 0.06 6 0.06 0.01 6 0.05 0.052 6 0.006 0.17 6 0.02 0.24 6 0.05 0.09 6 0.04

vy (mm/min) 0.18 6 0.04 0.14 6 0.01 0.17 6 0.02 0.25 6 0.05 0.25 6 0.02 0.17 6 0.02 0.12 6 0.07 0.22 6 0.04

3612 Hebert et al.


The two-photon microscopy images have been corrected for

an 8% bleedthrough of the ECFP signal into the EYFP

detection channel, as had been determined from control mea-

surements on cells expressing just ECFP a-actinin or EYFP

a5 integrin alone. We found that a5 integrin and a-actinin

are actively transported as a complex in some regions of

the cell (see Fig. 10), with an average transport velocity of

0.16 6 0.03 mm/min. Moreover, non-zero temporal cross-

correlation functions were calculated for a5 integrin and

a-actinin outside of visible focal adhesions (for example, in

region 2 of Fig. 10), meaning that both components that are

known to interact in mature adhesions are also present as

co-transported microcomplexes throughout the cell as we

have reported recently (Wiseman et al., 2004). In this study,

however, we have added the directional measurement and

obtained vectors via STICCS analysis for the co-localized

flowing populations.

CONCLUSION

We have shown that STICS, along with ICS, are powerful

tools for the investigation of protein dynamics and inter-

actions, and that STICS provides a way of measuring full

directional velocity vectors in the case of concerted macro-

molecular flow. The applications are not limited by ex-

pression levels in the cell, since this technique does not rely

on optically resolving and tracking individual molecules, and

they do not require any special labeling approaches. Using

STICS with ICS, we can distinguish between diffusion,

protein flow in random directions, directed flux in a single

direction, or a combination of these transport modes. By

employing Fourier-filtering with the STICS analysis, we can

effectively perform these measurements even in cell mem-

brane environments where there are significant levels of

immobile proteins (.90% immobile fraction, simulation

results not shown). Gaining directional information helps in

understanding complex phenomena such as adhesion forma-

tion and disassembly, membrane protein transport, and tran-

sport in polarized cell systems. The application of STICCS

to double-label cross-correlation experiments also promises

new insights into detecting molecular interactions and co-

transport of macromolecules in cells.

We acknowledge Prof. A.R. Horwitz and Dr. C.M. Brown (University of

Virginia) for kindly providing the transfected cell lines used in these studies

and for numerous insightful discussions. We thank Efraim Feinstein and

Jonathan Rossner for the original work on the simulation program. We also

thank Prof. Mark Ellisman (University of California at San Diego) for

allowing P.W.W. to perform some of the two-photon imaging at the Na-

tional Center for Microscopy and Imaging Research.

B.H. acknowledges a post-graduate scholarship from the Natural Sciences

and Engineering Research Council of Canada. P.W.W. acknowledges

funding in support of this work from the Natural Sciences and Engineering

Research Council of Canada, the Canadian Foundation for Innovation, and

the Canadian Institutes of Health Research.

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FIGURE 10 Two-photon auto- and

cross-correlation STICS velocity map

images of ECFP/a-actinin and EGFP/a5

integrin at the basal membrane of a CHO

cell on a fibronectin substrate. (A) STICS

velocity map for ECFP/a-actinin (channel

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The original image dimensions are 5123

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120 images at 5 s/frame.



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